room impulse response and deconvolution

[Martin Czech]

:::> Again room responses.
:::> 
:::> One of the problems is that I can not apply a unit impulse
:::> to the room. Balloons look more like differentiated unit pulses,
:::> and together with microphone far worse then that. So
:::> the recorded response is somehow convoluted with an unpleasant function.
:::> 
:::> One can try to deconvolute this, but the problem was, that:
:::> 
:::> 1. time domain deconvolution is impossible for fixed sequence length
:::
:::Hmm... this does not correlate well with my understanding here... please
:::elaborate so that I can understand who of us got something wrong (possibly
:::both ;).

Well, I should have said:  The measured balloon response b(n), the unknow FIR
filter coef.  a(n) and the unit impulse response (UI) u(n) (or some other wanted
sequence) give a system of linear equations (via matrix representation of
convolution).  It is obvious for me, that the number of equations is larger then
the number of a(n), furthermore the matrix has a diagonal appearance, eg.  a(0)
must be 1/b(0), this enforces a(1) and so on.  There is no solution for this
linear equation problem, so I derive from this that no such filter exists.


:::I assume that we are talking about stripping of the source impulse responce
:::from the sampled impulse responce. If this is what you mean I think that this
:::is fully possible in the time domain using cross-correlation. This is a simple
:::multiplication between the samples in a orderly fashion. It's simple math and
:::simple code but just expensive.
:::
:::If you see that I am of track, please enligthen me on that.

Now you got me! With respect the the application here I don't know
the interpretation for correlation (I know the mechanics of it's math,
though, fast corelation via fft should only involve taking H**S^ (the
conjugate complex spectrum) instead of H**S in my fast convolver.
Corelation is comutative, ie. H**S^ = S^**H, it should also be
= H^**S, so the best would be to conjugate the shorter wave.)

Cross corelation with what? I want to know, how the room response would look
like , if an unit impulse was applied. But this is not the case, because
the balloon free air impulse (BFAR) looks awfull. So I assumed, that tha whole room,
ballon, microphone, preamp, ADC arrangement is linear. The hope was, that
if I could find an inverse filter that converts the BFAR into a UI and that
this filter in turn will also restore the measured room response into
the ideal UI room response.

My understanding is the correlation gives the amount of equality between
two functions, or sequences, and when this appears, ie. for what shift. Do
you propose to corelate the room response with the BFAR?

In the moment I can not see how this will help me, but that's because
of my ignorance.

:::
:::I have been using cross-correlation techniques to measure impulse responces of
:::audio range. It is a well founded method and corrections can be applied.
:::This is also the method I proposed earlier in order to measure impulse
:::responces of rooms etc.

AFAIK this means: s1(n) is the direct signal, s2(n) is the measured room 
response, now what is the interpretation of s1(n)#s2(n) (cross corelation).
Is it the ideal response?

:::
:::> 2. seems to not converge for infinite sequence length
:::> 3. frequency domain deconvolution operates circular, ie.
:::>    expects the deconvolution filter only to work with circular
:::>     convolution, which is not what we need.
:::>     
:::> After running arround in the woods for a couple of hours I thought
:::> that linear convolution yields the same result as circular, if
:::> only the deconvolution filter is repeated again and again,
:::> of course, because this will mimic circularity for a while.
:::> 
:::> Ok, experimental software rewritten, cat copies 3 times the 
:::> deconvolution filter sequence, convoluted with the balloon free
:::> air response, voila, two nice sharp unit pulses in the middle,
:::> and of course some trash at the beginning and the end.
:::> But a silver lining. As you might have guessed, the next step
:::> is proper windowing, as always if abrupt sequnence ends have to
:::> be fixed. 
:::> 
:::> First experiments with a simple trapezoid window give encouraging results,
:::> a sharp unit impulse of magnitude 4000, and some garbage arround,
:::> but smaller then 50. 
:::> 
:::> The next steps should improve the window, and also verify that the garbage
:::> can not be heard because of masking by the big unit pulse.
:::> 
:::> So things get better.


Maybe this is similar to corelation??

:::> 
:::> The poor man's method (balloon) seems still to be reasonable for 
:::> acoustic measurements. 
:::
:::Here's a trick:
:::
:::You could use the direct sound from the balloon (up to the first reflection)
:::and use that and cross-correlate that to the full sample and by that remove
:::the balloons impulse responce from the rest in order to acheive a better
:::resulting room responce. The Achilles heel of this method is that you basically
:::assume that the impulse responce of the balloon as it pops is idealy the same
:::in all directions (which is isn't). It may be so that it is equalent enougth
:::so that the improvement is better.

Yes, and balloons differ..., but I think that is not so much problem.
I'm not interested in the REAL room response, a somewhat distorted response
that my ears can not distinguish from the REAL will be enough.
At the moment there is clearly too much hf damping.

:::
:::The same type of problem actually exist with every source. A balloon has
:::probably much tighter impulse responce diffrances than an ordinary speaker.
:::
:::Could anyone send me a self-freefloating pulsating sphere I could use?

I guess this is the sparc gap approach. But the two ball shaped electrodes
will certainly focus high frequency stuff, if they are not very small...

:::
:::> And for electronic measurements (electronic reverbs) I could
:::> try repeated pulses (signal enlarges by N^2, but noise only by N),
:::> so S/N can be improved (and is critical if it is hissing broad band
:::> noise).
:::
:::An interesting note here... an appropriate level of noise will help you get
:::over non-linearaties in A/Ds if you can do repeated measurements. Too low noise
:::level will let the non-lineareties come out, too high noise level will make
:::the noise come out (and thus require unecessary measurements to remove).

Must have written ...and is NOT critical if it is hissing broad band noise...
because this will not appear as noise, but diffusion, after my experiments.

m.c.